Using singular value decomposition to analyze drug/β-cyclodextrin mixtures: insights from X-ray powder diffraction...

The article discusses the use of mathematical models and linear algebra to understand the crystalline structures and interconversion pathways of drug complexes with β-cyclodextrin (β-CD). It involved the preparation and analysis of mixtures of indomethacin, diclofenac, famotidine, and cimetidine with β-CD using techniques such as differential scanning calorimetry (DSC), X-ray powder diffraction (XRPD), and proton nuclear magnetic resonance (¹H-NMR). Singular value decomposition (SVD) analysis is used to identify the presence of different polymorphs in the mixtures of these drugs and β-CD, determine interconversion pathways, and distinguish between different forms. In general, linear algebra or artificial intelligence (AI) is used to approximate the contribution of distinguishable entities to various phenomena. We expected linear algebra to completely reveal all eight entities present in the diffractogram dataset. However, after performing the SVD procedure, we found that only six independent basis functions were extracted, and the entities of the INM α-form and the CIM B-form were not included. It is considered that this is due to that data processing is limited to revealing only six or seven independent factors, as it is a small world. The authors caution that these may not always reproduce or approach reality in complicated real-world situations.